Topological components of spaces of representations
Integrity signals
Registry
Cites
Statistics
Claims the paper makes
Claims other papers make about this one
Each is checked against this paper’s own text: does it say what the citing paper says it does?
The space of homomorphisms (11) is not connected, and in general only one connected component gives the desired geometry.
“The space of homomorphisms (11) is not connected [148], and, in general, only one connected component gives our desired geometry.”
From Quantum Gravity in 2 + 1 Dimensions: The Case of a Closed Universe (2005) · cites this paper as [148]
Milnor-Wood inequality: for an S1-bundle over a closed surface T with structure group the orientation preserving homeomorphisms of S1 with the discrete topology, |e| ≤ 2g - 2 if g > 1, and e = 0 if g = 1.
“So | e | ≤ 2 g -2, if g > 1, and e = 0 if g = 1.”
From Lorentz spacetimes of constant curvature (2007) · cites this paper as [7]
If |e(ρ)| = 2g - 2 then ρ is discrete and faithful.
“Conversely Goldman shows in [6] that if | e ( ρ ) | = 2 g -2 then ρ is discrete and faithful”
From Lorentz spacetimes of constant curvature (2007) · cites this paper as [6]
Cited by
Sorted by citations
Lorentz spacetimes of constant curvature
Mess, G. (2007) · Geometriae Dedicata · doi:10.1007/s10711-007-9155-7 · Cited by 278 · see citing works
Quantum Gravity in 2 + 1 Dimensions: The Case of a Closed Universe
Carlip, S. (2005) · Living Reviews in Relativity · doi:10.12942/lrr-2005-1 · Cited by 172 · see citing works
Cosmological Time in (2+1) - Gravity
Benedetti, R., & Guadagnini, E. (2001) · Nuclear Physics B · doi:10.1016/s0550-3213(01)00386-8 · Cited by 43 · see citing works
Lorentz spacetimes of constant curvature
Mess, G. (2007) · arXiv · Cited by 5 · see citing works
- Authors
- Goldman, W. M.
- Affiliations
- University of Maryland, College Park (US)
- Corresponding author
- Goldman, William M.
- ORCID
- Goldman, William M.
- Venue
- Inventiones Mathematicae
- Published
- 1988-10
- Volume
- 93
- Issue
- 3
- Pages
- 557-607
- ISSN
- 0020-9910 (ISSN-L)
- 1432-1297
- OpenAlex
- W1976694540
- Cited by
- 350
- References
- 0
- Citations by year
- 2026: 10 · 2025: 7 · 2024: 13 · 2023: 12 · 2022: 8 · 2021: 10 · 2020: 12 · 2019: 23 · 2018: 11 · 2017: 12 · 2016: 25 · 2015: 19 · 2014: 16 · 2013: 16 · 2012: 16
- FWCI
- 2.64
- Type
- journal article
- Language
- en
- Open access
- closed
- Licence
- www.springer.com/tdm (tdm)
- Locations
- Inventiones mathematicae (publishedVersion)
- Topics
- Physical Sciences › Mathematics › Geometry and Topology › Geometric and Algebraic Topology
- Physical Sciences › Mathematics › Mathematical Physics › Advanced Algebra and Geometry
- Physical Sciences › Mathematics › Mathematical Physics › Homotopy and Cohomology in Algebraic Topology
- Keywords
- spaces of representation, algebraic groups, algebraic varieties, algebraic groups over non-closed fields, algebraic fundamental group
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
Are you an author, or do you see a problem with this page? Request a review
